数学建模论文分析解析

1、Team # 1570Page 17 of 17第三届“认证杯”数学中国数学建模国际赛承诺书我们仔细阅读了第三届“认证杯”数学中国数学建模国际赛的竞赛规则。我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。我们知道，抄袭别人的成果是违反竞赛规则的，如果引用别人的成果或其他公开的资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。如有违反竞赛规则的行为，我们将受到严肃处理。我们允许数学中国网站（）公布论文、以

2、供网友之间学习交流，数学中国网站以非商业目的的论文交流不需要提前取得我们的同意。我们的参赛队号为：1570我们选择的题目是：A参赛队员（签名）：队员1:魏祯队员2:李兴队员3:高安森参赛队教练员（签名）：无第三届“认证杯”数学中国数学建模国际赛编号专用页参赛队伍的参赛队号：（请各个参赛队提前填写好）：#1570竞赛统一编号（由竞赛组委会送至评委团前编号）：竞赛评阅编号（由竞赛评委团评阅前进行编号）：ThemostresoundingwhistleAbstract:Inthisreport,throughtheanalysisoffactorsaffectingthewhistlesoundin

3、gloudness,webuildgasunitaryflowmodelandmultistructuremodel.Inmodel1,usingthemassconservationequationandcontinuityequationofflowofenergyconservationin,obtainedthedensity,velocity,relationshipqualityforcewasestablished,sothattheenergytokeeptheoptimalcombinationofmaximum;inmodel2,throughthemethodofcont

4、rolvariables,tostudytheimpactofdifferentmouthsizeonloudness,simulateandrepeatedexperiments,thestructureandsizeofthewhistlebodythatthestrongestsound.Combinedwiththemodeltwoandmodel,wedesigntheloudestwhistle.Keywords:soundingloudnessgasunitaryflowmodelenergy conservationthe mass conservationIntroducti

5、on:Thewhistle,adevicewhichisthroughtheairquicklypressedintoanarrowspacewithinthedevicecausedbytheairflowdisturbance,soundingdevicetosendastrongsound.Whistleinthelifeandproductionhavebeenwidelyused.Trafficpoliceusingwhistlestoguidethevehiclethrough,soldiersthroughtheemergencybuzzertoachievetheaimofur

6、gentcollection,sportsevents,refereeingtodecisionsandguidancegamebywhistle,whenpeopleareindanger,theysendoutasignalofdistressthroughanintensewhistle.Sooftenthehighqualityofwhistlescanplayanimportantroleinproductionandlife.Socanwedesignasufficientlyloudwhistleisthekeytoimprovethequalityoflifeandproduc

7、tionefficiency?Assumptions:Thewhistlesoundiscausedbyairturbulencecausedbythevibration,theairflowofdifferentintensitywillaffecttheintensityofthesoundawhistle.Humidityandvelocityofsoundandtheairwhistle,thehumidityoftheairwillcausevaryingdegreesofimpactonairquality,soundquality,differentvelocityofairwi

8、llsendoutdifferentsounds.Thesoundandthegaswhistlebyfriction.Willcausefrictionwhistleacousticenergybodyloss,wouldseriouslyweakentheintensityofsound.Flowfieldsdisturbanceaffectedbythewhistlesound,differentairwilltakedifferentroutes,sothattheformationoftheflowfieldofdifferentdistribution,willcausethepr

9、essuredifferencesoccur,whichaffectstheintensityofthesound.Soundandwhistleonthematerials,differentmaterialshavedifferenttimbres,differenttimbreswillalsoaffecttheintensityofthesoundchange,so,changematerialcanalsocausetheintensityofsound.Aboutthereflectivityofsoundandacousticwhistleacousticreflectivity

10、assembly,reducesenergylossisreducedintheprocessofcommunication,whichwillincreasetheintensityofthesound.Thestructureandsizeofsoundandthewhistlebody,whistle,whistlebodyconcerned,differentstructure,itsinternalairflowwillformdifferentcanalsocausetheoccurrenceofdifferentstrengths,whistlingsizewillaffectt

11、heairflowreversalform,causesignificantinfluenceonthefrequencyofsoundandvibration,sothestructureandsizeofthewhistlebodyWillaffecttheintensityofthesoundawhistle.Problemanalysis: Problem1Themechanismofwhistleisacomplexprocess,improvewhistlesoundintensityalsoneedsomepracticalways.Whistlesoundintensityin

12、ternalandexternalfactors.Wesimulatethesoundofawhistlerelationshipbetweenthefactorsandthestrengththroughmodelingapproach.Wewillwhistletheairvelocityiscoupledtotheenergyequationandthequalityequation,causedbydifferencesintheenergyflowrateestablishedfordifferentcorrelationequationbetweenthetwo.Throughac

13、omprehensiveanalysisofallaspects,andadiscussionofthesimulationresultsofthemodel,andthusmoretargetedtoimprovethestrengthofthewhistlesound. problem2Throughthewhistlesoundintensityanalysisoftheactualsituation,wefoundthatmanyfactorswillaffectthewhistlesoundintensity.Whistlesoundvelocitygasintensity,stru

14、ctureandwhistleofthematerial,aswellasthedegreeofairflowdisturbancesrelatedtowhistle,buttheimpactofthesizeofthewhistlesoundintensityismoreobvious,therefore,ourimpactonthesoundofthewhistledimensionofintensitywereappropriatemodelsimulation,andmadeafurtherin-depthstudy.Wehavetostudythroughtheuseofmodeli

15、ng,andcontrolvariablesmethod,toexploretheextentoftheimpactonthesizeofwhistlewhistlesoundintensity.Bycontrollingthewhistlebodymakethesameamountofgasenteringandsonicvibrationimageissuedbysoftwaresimulationwhistle.VariableDeclaration:VLocalmeanvelocitynTotalfrictioncausedbyviscousandturbulentqHeatfluxi

16、ntensityFUnitmassforcePLocalpressureLocalairdensityTThelocaltemperatureVThestudyonthevolumeoffluidwithinthegiventimetSSurfacevolumeVvnThenormalvelocityFiTheareaofthesidecrosssectionalareaofAF2TheareaofthesidecrosssectionalareaofASpecificinternalenergyPerunittimeperunitmassreleaseofheatdWidthAAmplitu

17、deModelestablishments:Aseveryoneknows,therearealotofreasonsaffectingthewhistlesound,soundandgasflowvelocityofthewhistlegaveawhistlewhistle,structure,materials,elementsofsoundreflectivityandtheturbulencedegreehavecloserelationship.Theoccurrenceofwaveformfigurewhistle,wecanknowthewhistlewaveformissome

18、continuoussinewave,sohowtoincreasethewavecrestsortroughshasbecomethekeytoincreasethewhistlesound.ElLUULJLIlLlJUUlJLULl-UJIJJlJl-WlJ juUWUlJJULJ 0a 50100 ISO 200SofiesLeak*9t Factor 97.6 1%HixmMJpfl F regency Qx/皿”呷均FU*中辍钢ZmB #8Uvtabc won dF什 F 2；x F 2If the whistle side is free surface, then the fri

19、ction is zero, if whistle side is rigid, then the velocity is zero. Based on the above assumptions and simulation, we established a conservation equation between the change of normal stress and the speed and intensity of sound derived:(nv)ds = 0A、Assuming the mass force with potential energyf = ,v ：

20、( fv)dF = v ：(vv ：)dv =(： ：v) - ：v (;?v)dvgpContinuous equation by the conservation of mass- 、(：v) = 0,tFPP( fv)dv = . ? (v)dv, dvVVV ftdF，)vnds)dx-t2222Throughthediscussionofflowpropagationinsubsonicblowingthewhistle,whistleintheairenergy,andthendrawthesideeffectsontheenergylossoftheinternalparamet

21、ersofthewhistle,toanalyzetheoptimalschemetoreduceenergylosses.Accordingtooneyuanthegascontinuityequation,momentumequationisobtainedtherelationshipbetweenthevariousparametersaffectingthesound.Conclusionsaredrawnasfollows:thesizeofthefluidcompressibilityeffecttoacertainextent,sonic;thewhistlematerials

22、(communicationmedia)hasadirectinfluenceontheenergy;thesonicflowofgasisafunctionofstateparameters;inthetransmissionmediumtomaintainconsistentcase,sonicvelocityincreaseswiththetemperature.Model2Strength:Weusethemodel1groupusingphysicsequationanalysisoftherelationshipbetweentheflowvelocityandsound,andt

23、hewhistleissoundbecauseofthehigh-speedairflowfromarelativelynarrowgapflowcausedturbulence,thestructuresizehypothesiswhistlewillaffecttheacousticintensity.Inordertoanalyzetherelationshipbetweenthem,weestablishthemodelof2:inthecontrolofgasflowrateisconstant,bychangingthewidthanddiameterofthewhistle,th

24、edeterminationoftherelationshipbetweensoundintensityandtheir.Intensitydependsonthevibrationamplitudeoftheacousticsoundofthesize,thelargeramplitude,thegreatertheintensity;thesmallertheamplitude,theweakerthestrength.Weusevirtualinstrumentsoftwarethroughcomputermicrophonemeasuringamplitude,inordertored

25、ucetheerror,weusetheaveragevalueobtainedinsuccessive,changethewidthanddiametersizecase,multiplemeasurementsofamplitudeandtheaveragevalues.Table1Width(mm)Amplitude(mm)3.001005.0045010.0065015.0040020.0020025.0085TheamplitudeandwidthAmplitude/cmThe amplitude and widthWidth/mmFigure4:theamplitudeandwid

26、thWesimulatedtherelationshipbetweenthedatathroughtheMATLAB,clearlydrawnfromthediagram:whistleswidtheffectonamplitudeofthewhistlesounding:widerornarrower,smallersoundamplitude.whistlesdiameteraffectedthevocalamplitude:whistlediameterbiggerorsmaller,thesmallerthesoundamplitude.thesamewidthasthewhistle

27、,diameterislarger,thelowerthesamesoundamplitude;theinnerdiameterofthewhistle,thegreaterthemorewidth,lowsoundamplitude.whenthewhistlewidthanddiameterofbetween6and12mmlargeramplitudeModelapplicationandresultanalysisThroughtheanalysisonthemodelandtheprincipleofcalculusandanalytic,weconcludethatcanadjus

28、tthehighwhistlesoundloudnessmeasures,accordingtotheneedsofdifferentenvironmentsorsites,towhistlesoundloudnesswillhavedifferentrequirements,sowerang,therelationshipbetweendegreeandelementsaccordingtothewhistlesound,guideuschooseaccordingtotheirownneedsandselectthehighestwhistleinhisloudnessbytheappli

29、cationoftheplace4.Analysisbasedonabovemodel,weconsideredtheoptimalcombinationofvariousfactors,butalsowithreferencetothepreviousdesign,designedtheloudestvoicewhistle,whistleTongtisnailshape,length8cm,width6cm,thickness3cm,shapewithgentlecurves,theman-machineengineeringsciencebasedon,wefullyconsidered

30、handcomfort,sowillbethemostharmoniouscurveusedintheperipheryofthebodyofthewhistle.Themouthofthecirculardesign,likethisisadvantageouswhenusedwithstrictenoughcontactopening,reducetheblowoutgasleak,themouthandthewhistlebodywith1.8cmdistance,thisdistanceisconducivetothestabilityofairflow,reducethedistur

31、bance,thisisveryhelpfultotheentryandexitgasblowoutfromamorestable,thusthesoundofloud,continuous,concentration.Amplewhistlebodyspace,sothatyoucanmakemoreairinto,whenthesegaseswillbedischargedfromwhistlinghaveenoughloudness.Atthesametime,mustbeadequatespaceisstableairflow,whistlingintofromthegasaccumu

32、lationinthissufficientspace,thenthesteadyflowinthisspace,minimizetheflowdisturbance,helptoissuemoreforcefulvoice,thisenoughspaceforstoringenoughgasstoreupenoughenergy,whichmustbesoitiswithenoughsoundwhistle.Thentheairoutlet,inthisplaceweposttothisperiodofmaterialoutletgraduallythinning,makingtheoutl

33、etnearthewhistlebodyisthinenough,sofromthewhistlingintothewhistleandaccumulationofairflowcanmorequicklythroughtheairoutlet,andtheairflowcanstableisthewhistlebodycutting,voicefrequencythisproduceshigher,louder,withwhatwewantastrongenoughloudness.Figure5:whistlestereomodelFigure6:entityprofileStrengthsandweaknessesAccordingtotheanalysisofourqualitativeandquantitative,andthe